There is a substantial amount of NMR and x-ray data on the structure of RNA-peptide complexes. However, there is little information about the thermodynamics and dynamics of their formation. We propose to study the dynamics and thermodynamics associated with the formation of RNA construct peptide complexes using dual color fluorescence correlation spectroscopy (DCFCS) and single pair fluorescence resonance energy transfer (spFRET). This research will focus on bovine immunodeficiency virus trans-activating region (BIV TAR), BIV trans-activator peptide (BIV Tat), human immunodeficiency virus type 1 rev response element RNA construct (HIV-1 RRE), HIV-1 regulator of viral expression peptide (HIV-1 Rev) and their respective complexes. Our specific aims are: (1) Analyze the formation of BIV Tat peptide-BIV TAR RNA complexes. (a) Thermodynamics (deltaH, deltaG, deltaS) of complex formation. (b) Thermodynamics (deltaH, deltaG, deltaS) of modified complex formation. (c) Dynamics of BIV Tat peptide beta hairpin formation. (d) Dynamics of BIV TAR RNA groove formation. (2) Analyze the formation of HIV-1 Rev peptide - RNA complexes. (a) Thermodynamics (deltaH, deltaG, deltaS) of HIV-1 Rev peptide-RNA complex formation. (b) Dynamics of HIV-1 Rev peptide - RNA complexes. (c) Dynamics of HIV-1 RRE conformational changes with and without Rev peptide. The results of this study will contribute to understanding the dynamical process of RNA-peptide binding.